We introduce a refined differentially private (DP) data structure for kernel density estimation (KDE), offering not only improved privacy-utility tradeoff but also better efficiency over prior results. Specifically, we study the mathematical problem: given a similarity function $f$ (or DP KDE) and a private dataset $X \subset \mathbb{R}^d$, our goal is to preprocess $X$ so that for any query $y\in\mathbb{R}^d$, we approximate $\sum_{x \in X} f(x, y)$ in a differentially private fashion. The best previous algorithm for $f(x,y) =\| x - y \|_1$ is the node-contaminated balanced binary tree by [Backurs, Lin, Mahabadi, Silwal, and Tarnawski, ICLR 2024]. Their algorithm requires $O(nd)$ space and time for preprocessing with $n=|X|$. For any query point, the query time is $d \log n$, with an error guarantee of $(1+\alpha)$-approximation and $\epsilon^{-1} \alpha^{-0.5} d^{1.5} R \log^{1.5} n$. In this paper, we improve the best previous result [Backurs, Lin, Mahabadi, Silwal, and Tarnawski, ICLR 2024] in three aspects: - We reduce query time by a factor of $\alpha^{-1} \log n$. - We improve the approximation ratio from $\alpha$ to 1. - We reduce the error dependence by a factor of $\alpha^{-0.5}$. From a technical perspective, our method of constructing the search tree differs from previous work [Backurs, Lin, Mahabadi, Silwal, and Tarnawski, ICLR 2024]. In prior work, for each query, the answer is split into $\alpha^{-1} \log n$ numbers, each derived from the summation of $\log n$ values in interval tree countings. In contrast, we construct the tree differently, splitting the answer into $\log n$ numbers, where each is a smart combination of two distance values, two counting values, and $y$ itself. We believe our tree structure may be of independent interest.

In many biological systems, the developmental processes of individuals play a crucial role in shaping the traits, characteristics, and growth patterns of subsequent generations. Throughout various stages of growth and maturation, organisms undergo significant changes that impact their overall fitness and reproductive success. These developmental stages, ranging from early cellular differentiation to reproductive maturity, each contribute uniquely to the organism's ability to survive and transmit biological information to offspring. Conversely, hereditary processes also influence the developmental stages of subsequent generations, creating a feedback loop where the heritable traits and adaptations of individuals as well as their health statuses such as disease resistance, metabolic efficiency, or physiological robustness can impact the developmental trajectories of future generations. This feedback loop between developmental processes and heredity continually shapes evolutionary trajectories, driving adaptation and resilience in populations over time.

In this paper we show how to exploit interventional data to acquire the joint conditional distribution of all the variables using the Maximum Entropy principle. To this end, we extend the Causal Maximum Entropy method to make use of interventional data in addition to observational data. Using Lagrange duality, we prove that the solution to the Causal Maximum Entropy problem with interventional constraints lies in the exponential family, as in the Maximum Entropy solution. Our method allows us to perform two tasks of interest when marginal interventional distributions are provided for any subset of the variables. First, we show how to perform causal feature selection from a mixture of observational and single-variable interventional data, and, second, how to infer joint interventional distributions. For the former task, we show on synthetically generated data, that our proposed method outperforms the state-of-the-art method on merging datasets, and yields comparable results to the KCI-test which requires access to joint observations of all variables.

With rapid advancements in exoskeleton hardware technologies, successful assessment and accurate control remain challenging. This study introduces a modular sensor-based system to enhance biomechanical evaluation and control in lower-limb exoskeletons, utilizing advanced sensor technologies and fuzzy logic. We aim to surpass the limitations of current biomechanical evaluation methods confined to laboratories and to address the high costs and complexity of exoskeleton control systems. The system integrates inertial measurement units, force-sensitive resistors, and load cells into instrumented crutches and 3D-printed insoles. These components function both independently and collectively to capture comprehensive biomechanical data, including the anteroposterior center of pressure and crutch ground reaction forces. This data is processed through a central unit using fuzzy logic algorithms for real-time gait phase estimation and exoskeleton control. Validation experiments with three participants, benchmarked against gold-standard motion capture and force plate technologies, demonstrate our system's capability for reliable gait phase detection and precise biomechanical measurements. By offering our designs open-source and integrating cost-effective technologies, this study advances wearable robotics and promotes broader innovation and adoption in exoskeleton research.

An open problem in artificial intelligence is how systems can flexibly learn discrete abstractions that are useful for solving inherently continuous problems. Previous work in computational neuroscience has considered this functional integration of discrete and continuous variables during decision-making under the formalism of active inference (Parr, Friston & de Vries, 2017; Parr & Friston, 2018). However, their focus is on the expressive physical implementation of categorical decisions and the hierarchical mixed generative model is assumed to be known. As a consequence, it is unclear how this framework might be extended to learning. We therefore present a novel hierarchical hybrid active inference agent in which a high-level discrete active inference planner sits above a low-level continuous active inference controller. We make use of recent work in recurrent switching linear dynamical systems (rSLDS) which implement end-to-end learning of meaningful discrete representations via the piecewise linear decomposition of complex continuous dynamics (Linderman et al., 2016). The representations learned by the rSLDS inform the structure of the hybrid decision-making agent and allow us to (1) specify temporally-abstracted sub-goals in a method reminiscent of the options framework, (2) lift the exploration into discrete space allowing us to exploit information-theoretic exploration bonuses and (3) `cache' the approximate solutions to low-level problems in the discrete planner. We apply our model to the sparse Continuous Mountain Car task, demonstrating fast system identification via enhanced exploration and successful planning through the delineation of abstract sub-goals.

Given the growth in the variety and precision of astronomical datasets of interest for cosmology, the best cosmological constraints are invariably obtained by combining data from different experiments. At the likelihood level, one complication in doing so is the need to marginalise over large-dimensional parameter models describing the data of each experiment. These include both the relatively small number of cosmological parameters of interest and a large number of "nuisance" parameters. Sampling over the joint parameter space for multiple experiments can thus become a very computationally expensive operation. This can be significantly simplified if one could sample directly from the marginal cosmological posterior distribution of preceding experiments, depending only on the common set of cosmological parameters. In this paper, we show that this can be achieved by emulating marginal posterior distributions via normalising flows. The resulting trained normalising flow models can be used to efficiently combine cosmological constraints from independent datasets without increasing the dimensionality of the parameter space under study. We show that the method is able to accurately describe the posterior distribution of real cosmological datasets, as well as the joint distribution of different datasets, even when significant tension exists between experiments. The resulting joint constraints can be obtained in a fraction of the time it would take to combine the same datasets at the level of their likelihoods. We construct normalising flow models for a set of public cosmological datasets of general interests and make them available, together with the software used to train them, and to exploit them in cosmological parameter inference.

We introduce $\textit{Stein transport}$, a novel methodology for Bayesian inference designed to efficiently push an ensemble of particles along a predefined curve of tempered probability distributions. The driving vector field is chosen from a reproducing kernel Hilbert space and can be derived either through a suitable kernel ridge regression formulation or as an infinitesimal optimal transport map in the Stein geometry. The update equations of Stein transport resemble those of Stein variational gradient descent (SVGD), but introduce a time-varying score function as well as specific weights attached to the particles. While SVGD relies on convergence in the long-time limit, Stein transport reaches its posterior approximation at finite time $t=1$. Studying the mean-field limit, we discuss the errors incurred by regularisation and finite-particle effects, and we connect Stein transport to birth-death dynamics and Fisher-Rao gradient flows. In a series of experiments, we show that in comparison to SVGD, Stein transport not only often reaches more accurate posterior approximations with a significantly reduced computational budget, but that it also effectively mitigates the variance collapse phenomenon commonly observed in SVGD.

Dataset distillation (DD) is an increasingly important technique that focuses on constructing a synthetic dataset capable of capturing the core information in training data to achieve comparable performance in models trained on the latter. While DD has a wide range of applications, the theory supporting it is less well evolved. New methods of DD are compared on a common set of benchmarks, rather than oriented towards any particular learning task. In this work, we present a formal model of DD, arguing that a precise characterization of the underlying optimization problem must specify the inference task associated with the application of interest. Without this task-specific focus, the DD problem is under-specified, and the selection of a DD algorithm for a particular task is merely heuristic. Our formalization reveals novel applications of DD across different modeling environments. We analyze existing DD methods through this broader lens, highlighting their strengths and limitations in terms of accuracy and faithfulness to optimal DD operation. Finally, we present numerical results for two case studies important in contemporary settings. Firstly, we address a critical challenge in medical data analysis: merging the knowledge from different datasets composed of intersecting, but not identical, sets of features, in order to construct a larger dataset in what is usually a small sample setting. Secondly, we consider out-of-distribution error across boundary conditions for physics-informed neural networks (PINNs), showing the potential for DD to provide more physically faithful data. By establishing this general formulation of DD, we aim to establish a new research paradigm by which DD can be understood and from which new DD techniques can arise.

Multi-view classification (MVC) faces inherent challenges due to domain gaps and inconsistencies across different views, often resulting in uncertainties during the fusion process. While Evidential Deep Learning (EDL) has been effective in addressing view uncertainty, existing methods predominantly rely on the Dempster-Shafer combination rule, which is sensitive to conflicting evidence and often neglects the critical role of neighborhood structures within multi-view data. To address these limitations, we propose a Trusted Unified Feature-NEighborhood Dynamics (TUNED) model for robust MVC. This method effectively integrates local and global feature-neighborhood (F-N) structures for robust decision-making. Specifically, we begin by extracting local F-N structures within each view. To further mitigate potential uncertainties and conflicts in multi-view fusion, we employ a selective Markov random field that adaptively manages cross-view neighborhood dependencies. Additionally, we employ a shared parameterized evidence extractor that learns global consensus conditioned on local F-N structures, thereby enhancing the global integration of multi-view features. Experiments on benchmark datasets show that our method improves accuracy and robustness over existing approaches, particularly in scenarios with high uncertainty and conflicting views. The code will be made available at https://github.com/JethroJames/TUNED.

Training social event detection models through federated learning (FedSED) aims to improve participants' performance on the task. However, existing federated learning paradigms are inadequate for achieving FedSED's objective and exhibit limitations in handling the inherent heterogeneity in social data. This paper proposes a personalized federated learning framework with a dual aggregation mechanism for social event detection, namely DAMe. We present a novel local aggregation strategy utilizing Bayesian optimization to incorporate global knowledge while retaining local characteristics. Moreover, we introduce a global aggregation strategy to provide clients with maximum external knowledge of their preferences. In addition, we incorporate a global-local event-centric constraint to prevent local overfitting and ``client-drift''. Experiments within a realistic simulation of a natural federated setting, utilizing six social event datasets spanning six languages and two social media platforms, along with an ablation study, have demonstrated the effectiveness of the proposed framework. Further robustness analyses have shown that DAMe is resistant to injection attacks.